带指数参数的隐含波动率模型

Implied Volatility Model with Index Parameter

在广泛运用的Black-Scholes定价模型中,波动率被看作是一个固定的常数,但越来越多的实证分析表明这种假设在实际的期权市场中并不成立,隐含波动率具有"波动率微笑"和"期限结构"等特点。鉴于此,对Cassese和Guidolin提出的确定性隐含波动率模型进行改进,认为隐含波动率并不一定是关于在值程度的二次函数,采用指数参数项替代原模型中的在值程度二次项。最后基于AAPL股票期权进行实证分析,结果表明改进的模型更具灵活性,能更好地拟合和预测隐含波动率及期权价格。

In the widely used Black-Scholes pricing model,the volatility is assumed to be a fixed constant.However,more and more empirical analyses have proved this assumption is incorrect in the real option market,the implied volatility has two key features:volatility smile and term structure.This paper modifies the deterministic implied volatility model proposed by Cassese and Guidolin,it deems implied volatility is not necessarily the quadratic function of moneyness and replaces the quadratic term of moneyness with an index parameter term.With the modified model some empirical analyses based on AAPL stock option are carried out.The experimental results show that the modified model is more flexible and has a better fitting and forecasting ability.